Predicting S1 TDDFT energies from ZINDO calculations using Message-Passing Delta-ML with electronically-informed descriptors

We present a machine learning approach capable of enhancing the accuracy of Semi-Empirical excited state energy calculations with respect to Time-Dependent Density Functional Theory (TDDFT). Using a dataset of 10,000 organic pi-conjugated molecules calculated at the ZINDO and M06-2X/3-21G* TDDFT computational levels, we trained a model to learn the systematic errors of the low-level method and correct it towards higher-level accuracy values. The best performing model improved the correlation of ZINDO data from 0.75 to 0.95 on a test set of S1 TDDFT target energies, which is consistent with the correlation between TDDFT and experiment. Our model presents a negligible additional cost to ZINDO (0.02 ms per molecule), enabling the computational screening of large datasets of molecules using Delta-ML-enhanced-ZINDO calculations. Critical to the performance of the model is the AttentiveFP Message-Passing Neural Network with added electronic information derived from ZINDO calculations, such as particle-hole densities from the transition density matrix. We also investigate the utility of the Morgan fingerprint and a newly introduced descriptor for the electronic structure of molecules; a molecular orbital weighted radial distribution function. The possible applications of this Delta-ML approach in virtual screening projects are discussed.